Ok, you have three question in one here. I try to answer all of them.
1) It depends how you want to come to Liechtenstein. Basically, there are two options: by car or by train.
To get to Liechtenstein by car, you would leave Munich on the A96, travel trough Memmingen to the German border town Lindau. Then you cross into Austria, but leave Austria again at Hohenems to cross into Switzerland. In Buchs or Sevelen, you leave the Swiss highway and cross over the Rhine into Liechtenstein. Be careful, for both the Swiss and the Austrian highways you need toll stickers. The shortest period is 10 days in Austria and 1 year in Switzerland. The whole journey will take around 3 hours (depending on traffic and where exactly in Munich you start).
If you decide to take the train, you should look for the connections to Buchs SG (Switzerland) or Feldkirch (Austria) since Liechtenstein has no real train station. From both towns, it's only a short bus ride to Liechtenstein and the buses leave at least every half an hour. For example, you could take the connection that take 3:57. For this, in Munich, you take the train towards Zurich HB and get of in St. Magrethen (Switzerland). From there, take the train towards Chur (Switzerland) and get off in Buchs SG. From there, it's a 5 to 10 minutes bus ride into Liechtenstein. Checkout www.ssb.ch for train schedules (also covers Liechtenstein buses) and www.liemobil.li. Be careful: in the evening the connection might be scarce and take way longer.
There are also daily buses going from Munich to Zurich (http://meinfernbus.de/). Maybe taking such a bus to Zurich and then the train to Sargans or Buchs SG is also an option.
You might also want to check out this site that summarizes alternatives to travel to Liechtenstein.
2) It depends what you want to do. Liechtenstein is particularly famous for its mountain areas. So if you want to go hiking or skiing, one day is probably a little bit tight, but definitively doable. Other than that, you can visit the pedestrian area in Vaduz, the art museum and the castle in Vaduz and probably just cruise through the whole country to get a glimpse. Also try to go up to Triesenberg and/or Malbun to get a view about the Rhine valley. For this, a day is more then enough.
3) I'm not sure if such a card exist. But there is a tourist office right in the center of Vaduz (opposite of the post office). Probably you could go there and just ask. There is a bus ticket for 24h available.